Question

One end of a cylindrical rodmade from the material of refractive index 1.42 is hemispherical. A narrow beam of parallel rays is incident as shown in the figure. At how much distance will this beam of ray be focussed from the hemispherical surface ?

Answer 1

One end of a cylindrical rodmade from the material of refractive index 1.42 is hemispherical.
a narrow beam of parallel rays is incident as shown in the figure.


Here , u = ∞ , $\mu_1$=1 , $\mu_2$ = 1.42 , radius of curvature = R .

$\frac{\mu_2}{v}-\frac{\mu}{u}=\frac{\mu_2-\mu_1}{R}$

$\implies\frac{1.42}{v}-\frac{1}{\infty}=\frac{1.42-1}{R}$

$\implies\frac{1.42}{v}-0=\frac{0.42}{R}$

$\implies v=\frac{1.42R}{0.42}$

v = 3.381R